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The OP decribes exhaustive and mutually exclusive cases, with two options or outcomes. In statistics, this segmentation of the possible outcomes is often called a categorical variable. When the variable only takes two values, it is generally termed:

binary (already proposed by @Malvolio), for "appearing in pairs" (not directly related to the binary or base-2 number system) or Bernoulli variables. The related categories are often denoted by values 0 and 1 (very "binary" in the logical or computer sense), or 1 and 2.

or

dichotomous variables (which was proposed by @plagueheart, and I did not see at the time of my answer), from greek dikhótomos, “cut in half” or "cut in two".

Sometimes, categorical variables are segmented into: nominal, ordinal or dichotomous. Sometimes, people use "categorical variables" only for cases of three or more possible outcomes (multi-way, n-ary or polytomous), as opposed to 2-ary case.

Binary and dichotomous are sometimes considered synonyms. They both contains the root 2 (di- or bi-). For some, binary variables form a sub-species of dichotomous variables, whose values are assigned either a 0 or 1 label or binary state. The -tomy ("to cut", like in atom, with privative "a-", which cannot be cut) in dichotomy seems more precise than the concept of arity, that denotes two objects or operands ("binary stars", "binary operation"), without clear reference to the mutual exclusion.

With 0 or 1 binary labels, it remains possible to perform mathematical operations on variables (like averaging) and to quantize or dichotomize the result afterward, while it is more difficult to "average" red and not-red dichotomous categories.

[EDIT] After some comments, one can wonder about the correct use of "binary" vs "dichotomous", the latter being at first glance the correct one. However, the use of binary is widespread. I tend to consider "binary" as a metonymy for the dichotomous case, as illustrated in the Yin-Yang symbol:

There are two categories: the shady side (yin), and the non-shady or sunny side (yang). They are mutually exclusive (although intricated and dual). But one could describe them has black and white, with colors represented by 0 and 1. In other words, labels 0 and 1 somehow encode the two possible outcomes, and the 0 and 1 symbols inherit from the mutually exclusive nature of the binary numbers.

In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false. A logic satisfying this principle is called a two-valued logic or bivalent logic.

used to refer to a ​situation in which there is a ​choice between two
different ​plans of ​action, but both together are not ​possible:It's an either-or situation - we can ​buy a new ​car this ​year or we can go on ​holiday, but we can't do both.—
http://dictionary.cambridge.org/dictionary/english/either-or

You can describe your attributes as discrete. That is, the attributes may take on values from a (limited) set of distinct values, and no other, not even those that appear to fall between adjacent valid values.

One non-scientific word would be "Manichean", meaning to divide everything into the categories of good or evil. Stemming from religion, it would be used when the context is religious, moral, philosophical, maybe psychological.

The situations described in the original question are examples of a 'disjunctive' (which can act as an adjective as well as a noun). The word comes from Latin, and it means 'to separate exactly into two disjoint parts'.

If your evaluation of a person shifts only between admiring or loving them to despising or hating them you are said to be splitting. This is a common feature of personality disorders, but BPD or borderline personality disorder in particular (and usually includes the same kind of diametric shift in self-image as well, e.g., believing oneself to be superior, then feeling wortheless at another time). I just noticed @Kevin Workman already mentioned splitting, but I'll leave my elaboration (as possibly useful as a brief summary of the concept).

Binary is probably the most generally used specific term for an either-or possibility, I agree (with @Malvolio). It is becoming fairly common outside strictly engineering applications, e.g., "a simple binary decision based on prior conduct eliminates consideration of the finer detail of history."

A better technical term than binary (which can too easily be misused) is satisfies a zero-one law. This is a standard term in probability, and (roughly speaking, actually very roughly speaking) means all or none.

enumerated

In this case, your options are enumerated. This is also useful when the options are "Yes, No, or Maybe". For instance, you might not want "Yes, No, Probably, Possibly, Darned Sure, Booked The Ticket But Also Have A Big Meeting The Day Before So I Bought Ticket Insurance Just In Case"... just lump everything else into maybe.

In statistics, the term qualitative (as opposed to quantitative) is often used. It is generally regarded as synonymous with 'discrete' and 'categorical', which have also been suggested. The term refers to the type of data being captured, in this case whether a quality is present (1) or absent (0). For example, in a collection of subjects in an analysis, one might measure the amount of vitamin C they consume over a period (quantitative), vs whether they contracted a cold at all (qualitative). Qualitative data need not be binary, e.g. sex/gender, age category. Hence the overlap with 'categorical'

If something is unambiguous, there are no two ways to interpret it. If your girlfriend burns all your letters, texts you that she hates you, and moves a thousand miles away, the unambiguous message is that she’s finished with you.

Having or exhibiting a single clearly defined meaning

Admitting of no doubt or misunderstanding; having only one meaning or interpretation and leading to only one conclusion

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